Question

1. From approximately 500 B.C. to 80 A.D., the Roman Empire expanded their control of the Italian

peninsula. By 44 B.C. the Romans power had expanded to Spain, Macedonia, Asia Minor, Gaul,
North Africa and Greece. According to census records, the population, P in Rome in 500 B.C.E was
only about 310,000. With the expansion of the empire, the population increased at a rate of 85% per
year.
a.
Write a function that can be used to determine the population after t years. State and explain the
meaning of the values used to create the function in the context of the question.

Answer 1

The function to determine the population after a certain number of years is P(t) = 310,000 * 1.85^t, where P(t) represents the population after t years.

Step-by-step explanation:

To determine the population after t years, we can use the formula P(t) = P0 imes (1 + r)t, where P0 represents the initial population, r represents the growth rate as a decimal, and t represents the number of years.

In the given scenario, the initial population in 500 B.C. was 310,000, and the population increased at a rate of 85% per year. Therefore, the function to determine the population after t years would be P(t) = 310,000 imes 1.85t.

To find the population after a specific number of years, simply substitute the value of t into the function.

Answer 2

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